Model, depolymerization

Fig. 4. Coal depolymerization model of bituminous coal by Shinn.

Figure 5a reveals that this depolymerization model shows trends consistent with data but is not particularly accurate. However, a modified model was developed in which die right-hand side of Equation [5] was multiplied by a first-order reactivity term, a = with a being the reactivity, ka a proportionality constant, and t the time, and application of this model did a much better job of describing the time course of xylan hydrolysis, as shown in Figure 5b. The fact that declining bond reactivity describes the data well suggests that the original assumption that all xylan bonds are broken equally at random is not valid. An obvious next step is the determination of individual bond energies within the hemicellulose molecule and incorporation of this information into a modified model.

Figure 5. Comparison of an unmodified and modified depolymerization model applied to batch hydrolysis of com stover at 140 with 0,5% sulfuric...

A predictive macromolecular network decomposition model for coal conversion based on results of analytical measurements has been developed called the functional group, depolymerization, vaporization, cross-linking (EG-DVC) model (77). Data are obtained on weight loss on heating (thermogravimetry) and analysis of the evolved species by Eourier transform infrared spectrometry. Separate experimental data on solvent sweUing, solvent extraction, and Gieseler plastometry are also used in the model. 

Since the depolymerization process is the opposite of the polymerization process, the kinetic treatment of the degradation process is, in general, the opposite of that for polymerization. Additional considerations result from the way in which radicals interact with a polymer chain. In addition to the previously described initiation, propagation, branching and termination steps, and their associated rate constants, the kinetic treatment requires that chain transfer processes be included. To do this, a term is added to the mathematical rate function. This term describes the probability of a transfer event as a function of how likely initiation is. Also, since a polymer s chain length will affect the kinetics of its degradation, a kinetic chain length is also included in the model. 

Besides the main depolymerization reactions, side reactions should also be considered in the kinetic description of a PET recycling process. This is emphasized by the results obtained from a PET extrusion model [85] shown in Figures 2.19-2.23. The complete set of reactions summarized below in Table 2.10 have been used, but shear effects have not been taken into account. Chain degradation, accompanied by a significant reduction of intrinsic viscosity, occurs even within residence times of a few minutes. Carboxyl end groups, vinyl end groups and acetaldehyde are formed in amounts depending on residence time, temperature and initial moisture content of the PET flakes. 

While the chance of a systemic error in the modeling is always possible, the greatest variability, and uncertainty, is in raw material cost for depolymerization and the valuation of the product. Roughly speaking, the variable conversion costs,... 

The metal-catalyzed amplification of e.e. in small molecules, demonstrated by Soai and coworkers, along with the chiral enrichment of amino arid polymers by sequential polymerization/depolymerization steps, have shown that small enantiomeric excesses in nearly racemic mixtures can be reactively amplified to produce chiral dominance. These real chemical systems, which include plausible prebiotic reactions, experimentally demonstrate the principle of the chiral amplification of a spontaneously broken chiral symmetry in a dynamic and authentic chemical milieu. Therefore amplification to dominance of a small chiral excess of both small and polymeric molecules can be credibly incorporated into an origin-of-life model. 

Co catalysts, metal crystallite size and support effects, 39 242-246 Ru catalysts, metal crystallite size and support effects, 39 237-242 Thiele modulus effect, 39 275 reaction-transport models, 39 222-223 readsorption probability, 39 264-265 secondary chain growth, hydrogenation, and depolymerization reactions, 39 224—225... 

Summary of Proposed Models for Microtubule Assembly from Depolymerized Microtubule Protein... 

This theory clearly predicts that the shape of the polymer length distribution curve determines the shape of the time course of depolymerization. For example Kristofferson et al. (1980) were able to show that apparent first-order depolymerization kinetics arise from length distributions which are nearly exponential. It should also be noted that the above theory helps one to gain a better feeling for the time course of cytoskeleton or mitotic apparatus disassembly upon cooling cells to temperatures which destabilize microtubules and effect unidirectional depolymerization. Likewise, the linear depolymerization kinetic model could be applied to the disassembly of bacterial flagella, muscle and nonmuscle F-actin, tobacco mosaic virus, hemoglobin S fibers, and other linear polymers to elucidate important rate parameters and to test the sufficiency of the end-wise depolymerization assumption in such cases. 

The generality of the end-wise depolymerization kinetic model is indicated by the comparison of the observed and predicted time-courses of cold-induced microtubule disassembly (Fig. 3). See Self-Assembly Protein Polymerization... 

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